from tensorflow.examples.tutorials.mnist import input_data
import tensorflow as tf
mnist = input_data.read_data_sets("MNIST_data/",one_hot=True)

## model 
# y = softmax(W.x + b)
x = tf.placeholder(tf.float32, [None, 784]) # None stands for any
W = tf.Variable(tf.zeros([784, 10]))
b = tf.Variable(tf.zeros([10]))

y = tf.nn.softmax(tf.matmul(x,W) + b)

# entropy H_{y} = - \sum_{i} y_i \log(y_i)
y_ = tf.placeholder(tf.float32, [None, 10])
cross_entropy = tf.reduce_mean(-tf.reduce_sum(y_*tf.log(y), reduction_indices=[1]))

# train
train_step = tf.train.GradientDescentOptimizer(0.5).minimize(cross_entropy)

# do it
sess = tf.InteractiveSession()
tf.global_variables_initializer().run()
for _ in range(1000):
	batch_xs, batch_ys = mnist.train.next_batch(100)
	sess.run(train_step, feed_dict={x:batch_xs,y_:batch_ys})

## evaluation
correct_prediction = tf.equal(tf.argmax(y,1),tf.argmax(y_,1))
accuracy = tf.reduce_mean(tf.cast(correct_prediction, tf.float32))
print(sess.run(accuracy,feed_dict={x:mnist.test.images, y_:mnist.test.labels}))